It doesn’t fail in dia 46. Who said you can’t take your time to capture all? Take your time, capturing pièces after pièces and finally the whole. Black trying to save by connecting will not help either. You will finish by capturing all, no matter what black does.
What matters here is that white thought to have many eyes but only one was real.
Perhaps it’s clearer to ditch the idea of “save” entirely, as it can be misconstrued to mean of the group as a whole rather than a chain of stones in atari, and in the connect-and-die case even connecting them still doesn’t save the chain for the next move. So how about:
A false eye is an empty space which you could fill in by connecting in response to an atari on some surrounding stones.
I’m really trying to focus on the connecting and filling it in meaning it’s no longer an empty space and thus clearly not an eye, because that’s the intuition a beginners needs to train to get the concept at an intuitive rather than technical definition level. An empty space is not empty if you can be made to fill it in!
The delivery of basic things is sometimes not that obvious.
You don’t need to surround all the stones of the black group to capture the bottom part at A or B. If the lower part is surrounded black cannot save those stones. Therefore both eyes are false. To catch the rest of the group at C (the true eye) the group has to be surrounded completely
@Issa_T I didn’t express myself well. When I said “surrounding everything” I meant just one chain, just like you did. So, the lower 3 stones can be put in atari with just 3 stones and there’s no way to save them. This aligns with my internal definition. And I have an intuition that the upper “a” is also a false eye, but I can’t explain why, if someone asks me. There isn’t a way to put the upper “a” in atari directly, that was my question, which leads to …
@martin3141 You’re idea of a “chain of causality” is appealing to me. With that in mind, I would be satisfied to say that the the upper “a” is also false and the definition would be that, in the domino effect, the real eyes would be the last survivor(s).
Ps: I still need to read more carefully @gennan , @Uberdude and @Groin 's answers, when I have more time. I believe the definition that I want can be extracted around here. I saw some convoluted ones.
@AllanFelipe my previous post was not meant as a definition, rather a motivation and explanation of the difference between (false) eyes with respect to the given example. As a complete definition, I think that @gennan s answer is very good.
Here’s an example.
A and C are true eyes, whereas B is a false eye.
White can’t capture anything, so if we were to apply the definition
in the domino effect, the real eyes would be the last survivor(s).
we can’t really arrive at this conclusion.
To motivate the difference between A, C and B, consider what happens if Black fills in one of them.
If Black fills in A or C, then the whole group can be captured with two moves by White.
If Black fills in B, the group stays safe.
Here’s my definition of an eye:
An eye is an empty point surrounded by some of your stones, such that your opponent can’t stop you from connecting the surrounding stones without filling in the eye.
C is surrounded by black stones which are connected, and thus is an eye. For both A and B, the only way to connect the surrounding stones is filling them in, so they aren’t real eyes.
This accounts for two-headed dragons: for any of the “false” eyes in the cycle, the two halves can be connected by filling in other eyes “going the other way”. Note that you wouldn’t actually play these moves (or else you die), but you could, and your opponent could never stop the possibility.
Similarly for seemingly false eyes in seki - white can never block black from connecting at S2 (if white plays there, black captures everything, then connects S2). Again, black would not actually make this move in the game.
You have to be careful about having two eyes - here each of H2 and F2 is an eye individually, but with a move at G3, white can eliminate one of them.
I would call that two half eyes; I wouldn’t call them both eyes
If they are both half eyes, then the the black string should have only one eye and be dead - but black can live with a move, while white can reduce to one eye, so F2 and H2 together make an eye and a half.
good point. definitely not two eyes, though
Yeah. My point was that even if you have two shapes which look like eyes individually, they can still have a common weakness which means they aren’t really two eyes considered together.
In some way the shape are not complete. 3 of the 4 “corner points” have to be ensured but in your suggestion only 2 are. The other two aren’t by analysis as shown. I mean you can put it as a définition (3/4 ensured) which is sometimes easy (like with a stone or with another eye) and sometimes more complex like in your example but which is what to determine, what to look at and that’s the interesting fact about eyes, to be alive or dead and so to have something precise to check.
